Math 367 Homework Assignment 4
due Thursday, March 3
1. For each of the following sets of points in the Cartesian plane, determine whether it is
convex or not convex. For each that is not convex, justify your answer with an illustration.
F
♠
♣
2. Draw a picture of two convex sets whose union is not convex. (However, it is true that the
intersection of any two convex sets is convex.)
3. Let A, B, and C be three noncollinear points in the Cartesian plane R2 .
(a) Draw a picture to illustrate the interior of the angle ∠BAC. (Recall this is defined to be
the intersection of two half-planes.)
(b) Draw a picture to show that the interior of the triangle 4BAC is the intersection of three
half-planes.
4. Let A, B, and C be noncollinear points. Use the Angle Construction Postulate to show that
←→
there is a point D such that C and D are on opposite sides of AB, and µ(∠BAC) = µ(∠BAD).
Is there more than one such point D?
5. Do 3.3 # 4 a, b, c.
6. Do 3.4 # 1.
7. Do 3.4 # 2.